Differential Equations Answers

A uniform string of length l is struck in such a way that an initial velocity v0(constants) is imparted to the portion of the string between l/4 and 3l/4, while the string is in its equilibrium position. Find the subsequent displacement of the string as a function of x and t

The points of trisection of a tightly stretched string of length 30cm with fixed ends pulled aside through a distance of 1cm on opposite sides of the position of equilibrium and the string is released from the rest. Find an expression for the displacement of the string at any subsequent time. Show that the midpoint of the string remains always at rest.

A uniform string of line density rho stretched to tension rho.a^2 ,executes small transverse vibration in a plane through the undisturbed line of the string. the ends x=0 ; x= l of the string are fixed . Point x=b drawn aside through a small distance d and released at time t=0. Find the transverse displacement of any point of the string at any subsequent time.